Mass production and control technology now exists to
build telescope primary mirrors out of panels consisting of a large
number of small agile segments. This technology will deliver
diffraction limited performance without the need for additional
adaptive optics. There is no obvious limitation to the size
of telescope that can be built with this technology. A 25 meter version
is estimated to cost $250M and could be built within the next decade.
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Introduction

Over
the last two centuries, every increase in telescope size
by a factor of two has relied on using a new approach in technology.
Sometimes this was because of a fundamental limitation in the available
technology, but usually it was because it was too expensive, in both time
and money, to use existing technology. Scaling laws also suggest that big
telescopes are not cost effective without near diffraction limited
imaging. In the past, this meant retrofitting existing telescopes with adaptive optics. Although
telescope primary mirrors are usually figured to an accuracy of a few
tens of nanometers, the effect of atmospheric turbulence is to
introduce wavefront errors amounting to tens of microns of distortion
across the pupil. These distortions are currently removed using
expensive, high-performance adaptive optics (AO) systems increasing the
cost and complexity of the facility.

The biggest telescopes in the world use either monolithic, lightweighted mirrors (LBT) or an array of 1.8-meter size segments phased using edge sensors (Keck Observatory). Designers of the next generation of telescopes have concentrated on
scaling up these existing designs. The largest project, the E-ELT will build a 42 meter
primary mirror and use a total of five mirrors, including high order
adaptive mirrors 2.5 meters in diameter, to form the final image. However as the size of the telescope
increases the effect of gravitational distorting forces and wind
loading on the mirror becomes increasing severe; these problems drive
up the price and technical risk to the project. The total current cost
of three international telescopes, TMT, GMT, and E-ELT
planned to be built in the next decade is $3B with running costs
of over $200M/year. The current ELT designs are already near their limit in size and
affordability.

Astrophysics is moving to an era in which
statistical surveys of large numbers of faint objects are required to
distinguish between the increasing detailed theoretical models of the
evolution of the universe and galaxies. These projects require high
spatial resolution and enormous amounts of telescope time. We need to
build not just bigger telescopes but more telescopes of large
collecting areas that are affordable to build, simple to maintain and available to the
general community. More than ever, advances in observational
capabilities are going to be driven by access and cost and will require
innovation to achieve breakthroughs in telescope technology. This is
immensely challenging; the cost of a telescope is the sum of its parts
and even dramatic reduction in the cost of one of the system component,
such as the primary mirror, may not significantly impact the overall
cost. Breakthroughs have to be made across the board.
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Basic Principles of Adaptive Primary Telescope Technology

Advantages of Small Segments

In general, the overall weight of the telescope and
size of dome are important factors in reducing cost. The weight of a
telescope of given aperture is driven by the weight of the primary and
secondary optics, while the size of the dome is driven by the F-ratio
of the telescope and the level of wind loading that can be handled by
the primary and the telescope structure. Simple scales laws show that the smaller the
segments used to build the telescope, the lighter the primary mirror
becomes. We can also show that the depth of material that must be removed to introduce the required
amount of astigmatism and coma into the segment surface is given by:

Inasmuch
as fabrication costs tend to increase with the amount of optical work
required to produce the surface, this equations show that there is a
strong advantage in using smaller segments,
especially for fast primary F-ratios.The alignment tolerance
for skew of the segments on the backing structure are also reduced for
smaller segments. However, both TMT and E-ELT are designed to allow operation without high order
adaptive optics. The size of the segment then
becomes a compromise between the cost of making and supporting the
optics and perceived difficulty of controlling a large number of
segments. Reducing the size of segments by a factor of two
does not appear to
bring much benefit in cost if conventional manufacturing technology is
used. In a hexagonal structure there are only 6 segments
of the same shape and each one requires a substantial support
structure. As a result of trade studies, TMT and
E-ELT have chosen the same segment size of 1.44 meters, slightly
smaller than those used at Keck. Each segment will use a servo controlled 18 actuator warping
harness to improve the figure of each segment of the primary
mirror and three servo controlled actuators
to align the segments. The design of the actuators is non trivial since
each
segment weighs about 120kg/m^2 and must be positioned to a few tens of
nm.

However, as the segment size is reduced to about
0.3 meter, new methods of fabrication, testing and support are
possible and the use of small, agile segments impacts almost every
aspect of telescope design. At these sizes we can also literally
mass produce light-weighted segment, greatly simplify the support
structures and use low cost, highly reliable voice coils to move the
segments. These segments can then be assembled to form panels of
convenient size (typically 10 m^2) for installation on the telescope. Low
fabrication cost is only the first advantage of this technology. With
suitable control techniques, many of them already
necessary for the
conventional adaptive optics control in the telescope system, we can
take out
the effect of wind forces and atmospheric turbulence on the image
quality and build telescopes with faster optics and smaller domes. The
only downside is that the telescope is now totally dependent on
the control system, we are committed to "fly by wire " technology.
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Compensating for the Effects of Wind and Atmospheric Turbulence

The
forces required to move a segment so as to correct for atmospheric
disturbances are surprisingly small. Atmospheric turbulence displaces
the
wavefront by about 1 radian/coherence distance/coherence time. This
corresponds to a displacement of about 0.1 micron every 10 millisecond
for a 30 cm size segment. The mean acceleration under these conditions
is about
10^-3m/sec^2. We need to update the positions every millisecond if we
wish to correct for atmospheric
turbulence with a 100 Hz bandwidth. If we
assume that we have to move the 0.1 micron at a much faster speed of 1 millisecond (rather
than 10 millisecond) the force required during this time is
only 0.4N for a
2 kg segment and the average power needed to drive the segment is
still less than 20
mW. This conservative calculation shows that the maximum heat generated
by adaptive control of the segments will be < 1 watt/m^2, which
is less than the heat required to track typical fluctuations in
air temperature. The force and power levels required to correct
for wind are about
the same order. The high bandwidth of the system ( ≈
100 Hz) means
that:
(1) the controls system automatically corrects for
gravitational and wind deflections.

(2) also allows correction for the
effect for atmospheric turbulence on the wavefront so that an
additional adaptive optics system is not required.

(3) the primary
mirror shape no longer depends on the
stability of the backing structure.

Structural
deformations increase with telescope size. Because wind and atmospheric
turbulence follow a power
law, with more energy at lower frequencies, there is some
bending of the structure on largest spatial scales. The dynamic range
of the segment motion ( of order a few mm ) must be
sufficient to correct for structural deformation. The type of
material used for the backing structure is also important. The
movement of the segments to correct for wind and atmospheric turbulence
transmits energy into the backing structure
which must ultimately be dissipated as heat. Structural materials with
high damping, such as carbon fiber, are desirable
for this application and this technology is economic for light weight
segments.The
maximum displacement over a panel size of 4 meters is much less than
this ( typically < 50 microns )
and it is also possible to control each panel with a bandwith of order
1 Hz
to take out large scale deformations due to gravity and wind in some
hierarchical design.
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ATLAS ( Adaptive Telescope using a Large Array of Segments)

Introduction

ATLAS is an acronym for Adaptive Telescope using a Large Array of
Segments.
A CAD drawing, prepared by William Boettinger and Tom Fornek,
working at the Argonne National Laboratory, is shown left. ATLAS
is designed as a survey telescope aimed at statistical surveys
of objects at high red shifts. Most of the objects of interest are
galaxies or
proto galaxies with angular sizes of about 1 microradian and are thus
over-resolved at the diffraction limit of the telescope. For this
application the use of a single laser guide star provides sufficient
resolution
and wide field for the science goals at lowest cost and complexity. In the future, its field of view
can be expanded
at the expense of resolution by only correcting the ground layer. This
is useful for spectroscopic surveys in the visible and near
infra-red. Much higher performance will be obtained over
small angles using a bright star
as the wavefront sensing source. In this later configuration the
telescope will be able to search for, and image, planets orbiting other
nearby stars.
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Summary of the Design

ATLAS has a
circular entrance pupil 25 meters in diameter with a
central obscuration of 5 meters and primary mirror focal length of 20
meters. ATLAS is similar
in
appearance to large sub millimeter telescopes such as CCAT. The primary mirror consists of 84 panels arranged in a
radial
configuration. However,
instead of the panels being monolithic, they are build from between 38
and 72 segments each about 0.3 m square and each being able to be moved
over a distance of a few millimeters with a small signal bandwidth of
about 100 Hz. Each panel will weigh about the same as a single segment
of the Keck
telescope (400 kg) and will be about 6 m^2 in area. There are only 5
different types of panel. Replacement panels will be available and each panel will be designed to enable rapid
replacement for maintainence, recoating and repair. The primary mirror therefore consists of 4944 individual
segments, provide ~10,000 degrees of freedom. There will
typically be 32 different segment shapes, requiring the manufacture of
hundreds of identical segments. The backing structure that supports the
panels will be built composite material( black) and will itself be
supported by a steel azimuth structure. The secondary mirror is small
and highly lightweighted, so as to reduce the mass at the ends of the
secondary support structure. The outer two rings of panels
are clear of obstruction and avoid the entire pupil being divided into
discrete quadrants. This benefits adaptive control of the primary
mirror.
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Control of the Primary Mirror Surface

Discussion

The most important difference between ATLAS design and conventional
telescopes is that the control bandwidth of the segments is much higher
than the lowest resonances of the telescope structure. This is in
contrast, for instance, to Keck, where the structural
rigidly of the primary mirror is largely determined by the backing structure. The actuators that position
the mirror segments only correct for slow distortions of the structure
due to gravity or thermal effects. In the ATLAS design we attempt to control
the surface to an accuracy of a few tens of nanometers against a
backing structure that is compliant on medium and large spatial scales.
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Design of the Individual Segments

The original design of the segments used a lightweighted Pyrex
substrate, mounted on three, two point, wiffle trees. FEA
analysis enabled us to design a segment with a surface figure under
gravity of 15 nm peak to valley and a mass of 2 kg for a 32 cm square
substrate. A lever system
within each wiffle tree provided in an astatic support system, requiring minimal drive current to the voice
coils when under static gravity loads.

Lee Holloway, a professor at University of
Illinois at Urbana, modeled the response of the segment
to a command to a 1 micron step displacement ( blue line below). Also
shown are the response of its neighbors to this step input (insert).

A
compliant backing structure can
potentially introduce coupling between the segments. If one segment
position is changed in a step displacement, its control system applies
forces to the segment and reaction forces are transmitted to the
backing structure and thence to its neighbors. Lee modeled five
segments in a line on backing structure with an assumed compliance similar to
the ANL model.
The results are shown below left. This figure
gives the response of one segment to a step displacement (blue curve).
Also shown in the insert are the disturbances of neighboring
segments separated
by one through five segment distances due to this displacement.
Typical movement of neighboring segments are 10 nm and are damped out
in 20 milliseconds.

More realistic simulations, in
which the segments are directly exposed to 5 m/s winds were as undertaken by Professor Holloway. The wind power followed a von Karman
turbulent power spectrum with a break frequency of 0.3 Hz This simulations gave rms
segment motions of less than 15 nm. This wind speed corresponds to a
force of a few N/m2 and is considerably higher than the forces needed
to correct for atmospheric turbulence.

Several Pyrex
substrates were made for the project. However, the wiffle design is
relatively complex and its internal
resonances were shown to affect the servo performance. Also, because the back is
open, this design is not particularly strong for
its weight and Pyrex has sufficient thermal expansion to raise
potential problems. We have since developed and built a new technology
using pneumatic pistons as a support for a thin plate of zero
expansion material. The prototype system is shown below using 9 pistons
as the
support. These pistons are connected to the substrate via a magnetic
coupling, allowing the substrate to be removed for servicing. This
design also provides astatic support and a degree of internal
damping of the substrate. The pressure to the air
pistons is controlled so that the mean current sent to the voice coils
is zero.

A
prototype segment is
shown right. In this design a 3/8 inch plate is used as the segment
substrate. FEA analysis of the plate give a peak
to valley deflection of 10 nm under a vertical gravity load (see
below). 4 voice coils are used to
drive the segment in tip tilt and piston over a 5 mm distance. Use of 4
voice coils enables the segment to operate even
if one voice coil or drive fails. The servo is being designed so that
the segment will still operate, with some acceptable loss of
performance, if any one voice coil fails.

The cost
of voice coils, support and inductive sensors is estimated
at
$1K/segment in volume production. The cost of building panels from
these segments, including the servo systems, is predicted to be in the range $40K
to $50K/m^2.
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Optical Fabrication

A number of new polishing technologies have been proposed in recent
years aimed at high volume production of light-weighted mirror blanks.
The most conservative option, and the one chosen for the base plan, is
to use the Keck bend and polish technique, use a
spherical planetary lapping machine to polish the surface. For our segments, the direction of
astigmatism always lies along a radius vector, so it can be introduced
easily and accurately by applying a bending moment along opposite sides
of the segments prior to polishing. FEA analysis of this design gives a
fit of better than 100 nm to the ideal aspheric surface for all
segments types. We plan to make the faceplate of the segment slightly
oversize and cut it to the appropriate shape after polishing using a
water jet. Residual aberrations will then be corrected by Ion polishing
or similar technique. Nelson has reported that a 0.025 m diameter Ion beam can remove 5 x10^11 micrometer^3/day, so
that in principle we can process 600 m^2,starting with an initial surface error
of 200 nm, in less than 6 months with a single polishing station
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Optical Testing

Optical testing is a large part of the conventional cost of fabricating
mirrors. ATLAS has two important advantages compared to other
approaches. The 25m meter version of ATLAS uses only 32 different segment
shapes to make up primary and requires on average about 200
identical segments. The project will carefully prepare a
concave master for each shape and we have designed a testing
procedure that will make surface measurements with an absolute accuracy
better than 20 nm. These masters will be provided to the optical
fabricators and the profile of each segment shape will be measured
against this master using a Fizeau interferometer. This approach
will allow the project to provide the optical fabrication vendor with
known reference surfaces, greatly improving the certainty that the
optics are generated to the optical prescription and allowing multiple
vendors to fabricate the optics. Once the segments have been fabricated
they will be instrumented with edge sensors, assembled into panels,
aligned, and tested as a unit using a large flat as an autocollimator.
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Adaptive Optics Strategy

Adaptive
optics is an intrinsic feature of ATLAS technology and a requirement
for the science for which it is intended. No technical breakthroughs in AO technology and practice are needed, but a
reliable AO system is essential. In following sections we will discuss
specific approaches to critical subsystems including wavefront sensors
and laser beacons. In this section, we discuss our overall plan for a
staged implementation of ATLAS AO that will enable a productive science
program from first light.
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Stage 1: Natural Guide Star AO

The first
AO system used on ATLAS will use bright natural guide stars to
commission the system and carry out necessary on-sky development of
the telescope system. We would like to achieve a wavefront error
of 250nm early in the commissioning of ATLAS corresponding to a 65%
Strehl ratio at 2.4 micron. We expect to improve the performance for bright
sources to 150 nm (86% Strehl ratio at 2.4 micron) over time. However the main
goal will be to implement the single sodium guide star AO outlined
below.
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Stage 2: Single Sodium Guide Star AO

Many of the
science drivers for ATLAS can be achieved using a single laser guide
star. Although the cone effect degrades the on-axis Strehl ratio of a
laser guide star system, the field of view of correction is increased. This is
discussed in detail by Mathew Britten and Keith Taylor. In the first
figure, reproduced from their paper, shows the calculated value of d0
and a pictorial explanation of why the isoplanatic angle is increased.

The error due to
the cone effect is formally given by (Telescope diameter/d0)^5/3 in
units of rad^2. A telescope of diameter d0 has a wavefront error of 1
radian^2. The diagram on the right shows schematically that, for images
off- axis, at least some parts of the wavefront are better corrected
than for an AO system driven by a natural guide star. Britton and
Taylor calculate the point spread functions for an AO system limited by
the cone effect for various field angles and telescope sizes

The cone
effect is bigger for bigger telescopes. However, the
Strehl ratio improvement, between the Single laser guide star corrected image and
the seeing limited image, increases with telescope diameter . Although
the on-axis Strehl ratio is only 10% @ 1.65 micron with this
correction, the intensity of the diffraction-limited core of the image
is about two orders of magnitude greater than that of the
natural-seeing image over an arc minute field. The following table shows that ~50% of the light is
concentrated within a 0.1 arcsecond radius aperture on axis.

Field angle radius (arcsecond)

0.05 arcsec aperture

0.1 arcsec aperture

0

29%

49%

20

27%

41%

40

18%

36%

This performance means that the telescope can be efficiently coupled to a spectrograph or
integral field unit. We should also note that, although a 1 arcminute
field of view seems small, the resolution is still of order 10
milliarcseond in the near infra-red and that we will require about over
10000x10000 pixels to sample the field of view.
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Stage 3: Ground Layer AO (GLAO)

Much wider
fields can be obtained at visible wavelengths with some improvement
over non-AO performance, by only correcting the wavefront for ground
layer turbulence. We can achieve this using a single laser by nutating
the beam about the optical axis and providing image motion compensation
before the wavefront sensor. Rayleigh beacons provide an alternate
method of achieving this performance. At mid-latitude sites, GLAO can
reduce the width of the point spread function by 10-50%, depending on
distance from the optical axis, wavelength, and seeing conditions. Such
a modest reduction in performance requires careful
scientific justification. However gains could be much larger for sites
on the Antarctic Plateau, where the ground layer and boundary layer are
extremely thin and the free-air seeing is low, resolutions of 0.1
arcsecond over a 30 arcminute field of view appear possible. Such a
telescope would greatly outperform any planned telescope located at
other sites on earth.
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Stage 4: Multibeacon, Single/Multi DM laser guide star

Use of
multiple beacons will enable us to significantly improve imaging
performance. By using multiple beacons and wavefront sensors we can
reduce the cone effect. Using more beacons may not require more laser
power because the effect of spot elongation, which drives the laser
power requirement, can also be reduced with suitable placement of laser beams and control algorithms. Use of short pulse laser
systems may also provide increased performance with lower laser power,
although this technology still has to be developed. Although the most
efficient way
of reducing the Cone effect has yet to be worked out by the AO
community, multi laser guide star with a single adaptive primary should give a
wavefront error of between 100
and 150 nm over a field of view of a few tens of arcsecond. A small number
of natural stars are still required to implement this improvement,
limiting access to about 50% of the sky. In the more distant
future, the ATLAS primary mirror will be used correct for ground
layer turbulence and additional deformable mirrors (DMs) conjugate to
high-altitude layers will be located between the primary mirror and the
science instrument. This will allow us to have diffraction limited
imaging over a wider field of view. Planning for this mode will only
start once first generation systems have been successfully demonstrated
on existing 8 to 10 meter telescopes.
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Wavefront Measurement

There are a
number of different ways of providing the signals to control the
positions of the segments. The Keck telescope was designed to use only
edge sensors, but has very successfully also used Shack-Hartmann
wavefront sensors and a natural guide star to observe the relative positions of the edges of the
hexagonal mirror. This optical technique works well with broad band
sources, such as stars,
but can only determine the position, modulo half a wavelength, for
single frequency sources such as a sodium guide star. Extension of the
dynamic range can be made using a second wavelength, such as the
Potassium line guide star at 766 nm to achieve lock. The lower brightness of this
laser guide star is acceptable since we can use longer time scales to determine
the number of wavelengths shift between segment edges. We propose,
however, to use a combination of edge sensors
and an optical wavefront sensor provide the error signals. We are
developing a low cost wide band inductive sensor with a noise floor of
about 3 nm/√Hz. This will be used to provide edge sensing information,
measuring the differences between the corners of neighboring
segments. We will use a laser guide star to drive the optical
wavefront sensor.
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Laser Power Requirements

If a laser
is fired from a position close to the optical
axis, it will appear as an elongated image at the edge of the telescope
pupil ( the obliquity effect). A 15 meter telescope will have a maximum
laser guide star dimension of 2 arcseconds in the radial direction and
a 25 meter telescope over 3
arcsecond. To obtain an estimate of the laser guide star brightness
needed for the project we can carry out the following calculation. The
noise propagator of an optimal least squares estimator of the
wavefront, based on the number of measurements required (about
50,000), is 1.3 times the phase difference measurement variance
across a subaperture. A typical error budget for the wavefront
estimation is 60nm. Assuming that we can use edge sensors to
measure the
position difference of segments to 30 nm with a 100 Hz bandwidth, the
laser guide star wavefront system should be able to measure the phase
difference to 52 nm across a segment. This corresponds to an error in
determining the position of the laser guide star of 0.16
microradians. For a
single
beacon launched near the optical axis of the telescope, the obliquity
effect
produces a spot with about 10 microradians FWHM at the edge of the
field of a 15 meter telescope. This requires a signal/noise for the
position measurement of at least 60 over a measuring interval of a few
milliseconds. This topic is discussed in more detail on the laser guide
star page.

The reference
design will use the pulsed sum frequency laser technology
developed for Palomar Observatory. This laser currently operates at 8
watt, generating 150 microsecond long pulses at a 400 Hz
rep rate. The laser
upgrade for this project will provide additional solid state amplifiers
on the output stages of the
two IR
oscillators. It will improve the chirping and backpumping technology
already demonstrated at the Observatory and will run higher
frequencies. We
expect to obtain a return of at least 1 Million photons/sec/m^2/watt
with this laser, based on our current experience at Palomar, at a
sodium
column density of 4 x 10^13 atoms/m^2. For a 15 meter telescope under
conditions of low sodium abundance, we believe that we can obtain this
level of performance with a pulsed sum frequency laser with
chirping and back pumping generating 30-40 watts. Over 100 watts
of power will be required for a single beacon
controlling a 25 meter telescope and it seems likely that some multiple
beacon approach will be needed for telescopes of this size. All laser
guide star systems need a few faint, natural guide stars, to remove
very low order
wavefront errors and a comprehensive design study needs to be completed
to determine the best configuration of laser guides to remove the cone
effect.
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Telescope Structure

The
requirements for the telescope structure are similar to
those for telescopes designed for submillimeter wavelengths. We expect
to be able to draw on a reservoir of community, especially the 25 meter
CCAT, and industry expertise to aid in estimating costs and
fabrication times, so the risks associated with this part of the
project will be low.

A
conceptual design telescope structure was carried out at the Argonne
National Laboratory in 2005. This study gives some idea of the
design, weight and cost of the different parts of the telescope. The
primary mirror structure and secondary mirror supports are carried on a
square space frame made from carbon fiber, as is shown below. The four secondary support
arms are held at the edges of the square box structure and pass through
the primary mirror panels before meeting at an apex behind the
secondary mirror. The Alt-Az mount is a steel space frame structure.

The
segments are supported on a backing structure that contains the
electronics, cooling, and communication needed to drive the segments,
together, they form a modular panel. The panels are carried by the
primary mirror support truss, a 10-ton carbon-fiber structure attached
to the box frame. Cassegrain instruments will be
accommodated within a large volume near the center of mass below the
primary mirror. They will be mounted and demounted by means of an
elevator through a 6.5x6.5-m hole in the pier.
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The laser would
not have been built without the hard work of Viswa Velur ( CalTech) and
the advice and support of Antonin Bouchez and Richard Dekany (CalTech).
Partial funding for the laser at Palomar Observatory was provided by
Cal Tech.

Single laser guide star performance figures are taken from a paper "SLGLAO" by Matthew Britton and Keith Taylor ( Cal Tech)

Support of this
work by University of Chicago, Argonne National Laboratory and the
National Science Foundation is gratefully acknowledged.
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